Calculus/Limits/Exercises

← Proofs of Some Basic Limit Rules Calculus Differentiation →
Limits/Exercises

Basic Limit ExercisesEdit

1.  
 
 
2.  
 
 
3.  
 
 
4.  
 
 

Solutions

One-Sided LimitsEdit

Evaluate the following limits or state that the limit does not exist.

5.  
 
 
6.  
 
 
7.  
 
 
8.  
The limit does not exist.
The limit does not exist.
9.  
 
 
10.  
 
 

Solutions

Two-Sided LimitsEdit

Evaluate the following limits or state that the limit does not exist.

11.  
 
 
12.  
The limit does not exist.
The limit does not exist.
13.  
The limit does not exist.
The limit does not exist.
14.  
 
 
15.  
 
 
16.  
 
 
17.  
 
 
18.  
 
 
19.  
 
 
20.  
The limit does not exist.
The limit does not exist.
21.  
 
 
22.  
The limit does not exist.
The limit does not exist.
23.  
 
 
24.  
 
 
25.  
The limit does not exist.
The limit does not exist.
26.  
 
 
27.  
 
 
28.  
 
 
29.  
 
 
30.  
 
 
31.  
The limit does not exist.
The limit does not exist.
32.  
The limit does not exist.
The limit does not exist.
33.  
The limit does not exist.
The limit does not exist.

Solutions

Limits to InfinityEdit

Evaluate the following limits or state that the limit does not exist.

34.  
 
 
35.  
 
 
36.  
 
 
37.  
 
 
38.  
 
 
39.  
 
 
40.  
 
 
41.  
 
 
42.  
 
 
43.  
 
 
44.  
 
 
45.  
 
 
46.  
 
 

Solutions

Limits of Piecewise FunctionsEdit

Evaluate the following limits or state that the limit does not exist.

48. Consider the function

 
a.  
 
 
b.  
 
 
c.  
The limit does not exist
The limit does not exist

49. Consider the function

 
a.  
 
 
b.  
 
 
c.  
 
 
d.  
 
 
e.  
 
 
f.  
 
 

50. Consider the function

 
a.  
 
 
b.  
 
 
c.  
 
 
d.  
 
 

Solutions

Intermediate Value TheoremEdit

51. Use the intermediate value theorem to show that there exists a value   for   from  . If you cannot use the intermediate value theorem to show this, explain why.
Notice   is continuous from  . Ergo, the intermediate value theorem applies. For all  , there exists a   so that  
Notice   is continuous from  . Ergo, the intermediate value theorem applies. For all  , there exists a   so that  

External LinksEdit


← Proofs of Some Basic Limit Rules Calculus Differentiation →
Limits/Exercises